Fast Filtering in Switching Approximations of Nonlinear Markov Systems with Applications to Stochastic Volatility

We consider the problem of optimal statistical filtering in general nonlinear non-Gaussian Markov dynamic systems. The novelty of the proposed approach consists in approximating the nonlinear system by a recent Markov switching process, in which one can perform exact and optimal filtering with a linear time complexity. All we need to assume is that the system is stationary (or asymptotically stationary), and that one can sample its realizations. We evaluate our method using two stochastic volatility models and results show its efficiency.